An algebraic Monte-Carlo algorithm for the Partition Adjacency Matrix realization problem

TL;DR

This paper introduces an algebraic Monte-Carlo algorithm that efficiently solves the graphical realization problem for degree sequences and partition adjacency matrices, with polynomial runtime when the number of partition classes is limited.

Contribution

It formulates generalized versions of the realization problem and provides a polynomial-time Monte-Carlo algorithm for bounded partition classes.

Findings

Algorithm runs in polynomial time for bounded classes

Successfully generalizes the Exact Matching Problem

Provides a probabilistic solution method

Abstract

The graphical realization of a given degree sequence and given partition adjacency matrix simultaneously is a relevant problem in data driven modeling of networks. Here we formulate common generalizations of this problem and the Exact Matching Problem, and solve them with an algebraic Monte-Carlo algorithm that runs in polynomial time if the number of partition classes is bounded.